Related papers: On the speed of pulled fronts with a cutoff
For certain values of the wave speed parameter, evolution equations for the temperature of a region of fuel admit traveling wave solutions describing fire fronts. We consider such a system in the form of a nonlinear reaction-diffusion…
In the present article we consider the problem of underwater avalanches propagating over moderate slopes. The main goal of our work is to investigate the avalanche front velocity selection mechanism when it propagates downwards. In…
This paper is concerned with the analysis of speed-up of reaction-diffusion-advection traveling fronts in infinite cylinders with periodic boundary conditions. The advection is a shear flow with a large amplitude and the reaction is…
The dynamics of fronts, or kinks, in dispersive media with gain and losses is considered. It is shown that the front parameters, such as the velocity and width, depend on initial conditions. This result is not typical for dissipative…
Front propagation described by Huygens' principle is a fundamental mechanism of spatial spreading of a property or an effect, occurring in optics, acoustics, ecology and combustion. If the local front speed varies randomly due to…
The dynamics of a point charged particle which is driven by a uniform external electric field and moves in a medium of elastic scatterers is investigated. Using rudimentary approaches, we reproduce, in one dimension, the known results that…
The depinning of an elastic line in a random medium is studied via an extremal model. The latter gives access to the instantaneous depinning force for each successive conformation of the line. Based on conditional statistics the universal…
A reaction-diffusion model which is called the field-road model was introduced by Berestycki, Roquejoffre and Rossi [9] to describe biological invasion with fast diffusion on a line. In this paper, we investigate this model in a…
We propose a phenomenological description for the effect of a weak noise on the position of a front described by the Fisher-Kolmogorov-Petrovsky-Piscounov equation or any other travelling wave equation in the same class. Our scenario is…
We investigate the inside structure of one-dimensional reaction-diffusion traveling fronts. The reaction terms are of the monostable, bistable or ignition types. Assuming that the fronts are made of several components with identical…
We introduce a speed selection mechanism for front propagation in reaction-diffusion systems with multiple fields. This mechanism applies to pulled and pushed fronts alike, and operates by restricting the fields to large "finite" intervals…
The dynamics and stability of brittle cracks are not yet fully understood. Here we use the Willis-Movchan 3D linear perturbation formalism [J. Mech. Phys. Solids {\bf 45}, 591 (1997)] to study the out-of-plane stability of planar crack…
The motion of an elastic body over a rough surface is simulated in one dimension using Newtonian dynamics. We drive the body by prescribing a constant velocity. We extract the friction force from the work done by the applied force in order…
We consider a branching-selection particle system on $\Z$ with $N \geq 1$ particles. During a branching step, each particle is replaced by two new particles, whose positions are shifted from that of the original particle by independently…
The derivation of a Moving Boundary Approximation or of the response of a coherent structure like a front, vortex or pulse to external forces and noise, is generally valid under two conditions: the existence of a separation of time scales…
The motion of a particle in a correlated random potential under the influence of a driving force is investigated in mean field theory. The correlations of the disorder are characterized by a short distance cutoff and a power law decay with…
We study the phenomena associated with the low-velocity impact of two solid discs of equal size using a cell model of brittle solids. The fragment ejection exhibits a jet-like structure the direction of which depends on the impact…
We present a variational principle governing the quasistatic evolution of a linearized elastoplastic material. In case of linear hardening, the novel characterization allows to recover and partly extend some known results and proves itself…
We consider a modification of the fluid flow model for a tornado-like swirling vortex developed by J. Serrin, where velocity decreases as the reciprocal of the distance from the vortex axis. Recent studies, based on radar data of selected…
The effect of a drift term in the presence of fixed boundaries is studied for the one-dimensional Edwards-Wilkinson equation, to reveal a general mechanism that causes a change of exponents for a very broad class of growth processes. This…